[source] Glass-forming liquids, granular systems, colloids, emulsions and foams exhibit a huge increase in relaxation time while their structure is hardly affected. From the analogy between the glass, or jamming, transition and other phase transitions, one would expect to find a growing correlation length governing the slow dynamics; however this length scale remains elusive. One of the leading suggestions for a relevant length scale comes from the heterogeneity of the dynamics.
Granular and colloidal experiments have indeed demonstrated that as jamming is approached, the length scale over which the dynamics are correlated increases dramatically.
In molecular glass formers, on the other hand, a significant increase in this dynamic correlation length is typically followed by a range over which the relaxation time may grow by more than ten orders of magnitude while the spatial extent of heterogeneity in the dynamics increases by less than a factor of two.
We resolved this puzzle using the kinetically-constrained spiral model. Our tractable lattice model includes mechanisms that separately mimic the effects of density, temperature and non-equilibrium driving. Here, the ingredient responsible for slow dynamics is that the ability of a particle to hop between adjacent lattice sites depends on the occupation of neighboring sites in a manner that models the geometric setting constraining allowed moves in disordered particulate systems. We separated the effects of density, temperature and driving and showed that jamming resulting from increasing density gives rise to dynamic heterogeneity that grows unboundedly. Whereas decreasing temperature or driving strength eventually leads to a saturation of the dynamic correlation length even though the relaxation time diverges.
Jamming mechanisms and density dependence in a kinetically-constrained model
Y. Shokef and A.J. Liu
Europhysics Letters 90, 26005 (2010)